The puzzle associated with the cost of sex, an old problem of evolutionary biology, is discussed here from the point of view of nonequilibrium statistical mechanics. The results suggest, in a simplified model, that the prevalence of sexual species in nature can be a natural and necessary consequence of the discrete character of the nonlinear interactions between couples and their pathogens/parasites. Mapped into a field theory, the stochastic processes performed by the species are described by continuous fields in space and time. The way that the model's parameters scale with subsequent iterations of the renormalization group gives us information about the stationary emergent properties of the complex interacting systems modeled. We see that the combination of one aspect of the Red Queen theory with the stochastic processes theory, including spatiotemporal interactions, provides interesting insights into this old Darwinian dilemma.